Warnock believes that knowing his career at Anfield was on the line after a loan spell at West Brom last season was the fuel Sturridge needed to really get going again.
But Roberto Firmino came off the bench to snatch the points with a dramatic stoppage-time victor just days after suffering a nasty eye injury against Tottenham.
The Ligue 1 side were curiously inert for large swathes of the second half, with Liverpool's energetic defence doing a fine job of keeping Neymar, Edinson Cavani and Kylian Mbappe on the back foot. "We are suffering a little bit but that's not an excuse", said Tottenham manager Mauricio Pochettino.
Milner, 32, has landed a number of man-of-the-match awards and has received rave reviews in a blistering opening to the campaign which has raised hopes that Liverpool could land a first top flight title in 28 years.
Just 4 minutes after the Milner penalty, Bernat found some measure of redemption when his cross led to PSG's first goal of the day.
It was nearly 2-0 a minute later, PSG scrambling the ball away after excellent work from Mohamed Salah had created havoc, but Mbappe then missed a chance to level when he lifted over from inside the box.
Liverpool thought they had a third after the break when Mohamed Salah had the ball in the net but the effort was ruled out by referee Cuneyt Cakir who correctly ruled that Sturridge had fouled Areola when the pair scrapped for a loose ball. Firmino made that chance count.
Did Liverpool prove they can play with Europe's elite against PSG?
PSG are among the favourites for this season's competition but having started the Champions League in the same thrilling fashion that took his team to the final last season, Klopp insisted Liverpool's win confirms they are a match for anyone.